ax²+bx+c=0

The equation you've written, \( ax^2 + bx + c = 0 \), is a quadratic equation, where:

• \( a \), \( b \), and \( c \) are coefficients,
• \( x \) is the variable,
• \( a \neq 0 \) (if \( a = 0 \), the equation becomes linear).

To solve for \( x \), you can use the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Here’s a breakdown of the components:

• \( b^2 - 4ac \) is called the discriminant. It determines the nature of the roots of the quadratic equation:
  • If the discriminant is positive, there are two distinct real roots.
  • If the discriminant is zero, there is one real root (a repeated root).
  • If the discriminant is negative, there are two complex (imaginary) roots.

If you need help with a specific problem or further explanation about solving or graphing quadratic equations, feel free to ask!